Corrugated pipe that is commonly used for drainage of soil and transportation of surface water typically has a profile with sides of the corrugation that are fairly steep and a top or crest of the corrugation that is fairly flat.
There are two basic ways that pipe can fail in use: by deforming excessively or by fracturing. Stiffer material is less likely to deform but more likely to fracture under stress. Flexible material is more likely to deform but less likely to fracture under stress. Deformation is expressed as a ratio of elongation of the material to its original material length and is called “strain.” Stress causes the deformation that produces strain. The modulus, or stiffness, of a plastic is the ratio of stress divided by strain, or the amount of stress required to produce a given strain.
There are a number of ways to provide lower deformation of a pipe in use: (1) increasing pipe stiffness by using a stiffer material; (2) thickening the pipe walls; or (3) changing the wall design to increase the moment of inertia, which increases the overall stiffness of the pipe wall. Using stiffer material to make a corrugated plastic pipe is disadvantageous because the pipe must be able to deflect under load to a certain degree without cracking or buckling. A certain amount of elasticity is therefore beneficial in preventing brittle failures upon deflection.
Thickening the pipe walls is also disadvantageous because it adds material cost and increases weight to the pipe which increases shipping and handling costs. Thus, it is advantageous to find a wall design that increases the moment of inertia of the pipe, while causing a minimal increase to the weight of the pipe or the stiffness of the material used to make the pipe.
Increasing the moment of inertia of a pipe wall increases its resistance to bending. One example of a wall design that increases the moment of inertia, and therefore the stiffness, of a plastic corrugated pipe with minimal increase in pipe weight and material stiffness is illustrated in U.S. Pat. No. 6,644,357 to Goddard. In this pipe, the ratio of height of a corrugation to the width of that corrugation is less than 0.8:1.0, and the sidewall of the corrugation is inclined, with respect to the pipe's inner wall, in the range of 75-80°. This ratio allows the pipe to deflect to greater than 30% of its original diameter without exhibiting imperfections associated with structural failure.
Pipe failure can be prevented by minimizing the maximum force exerted on the pipe walls during the bending associated with deformation. If a sheet of material, such as plastic, is flexed, the outside of the resulting curve is deformed in tension, and the inside of the curve is deformed in compression. Somewhere near the middle of a solid sheet is a neutral plane called the centroid of the sheet. In the case of corrugated pipe, the “sheet ” thickness comprises corrugations to achieve economy of material. Because the “sheet ” is therefore not solid, the centroid may not be in the middle of the sheet, but rather is located at the center of the radius of gyration of the mass (i.e., the centroid is displaced toward the location of greater mass). The more offset the centroid is from the middle of the sheet thickness, the greater the maximum force will be at the surface farthest from the centroid during bending or flexure from deformation due to a longer moment arm for certain acting forces. Thus, to lower the maximum force caused by pipe wall deformation, the pipe should be designed so that the centroid is closer to the middle of the sheet thickness. The closer the centroid is to the middle of the sheet thickness, the more desirably uniform the stress distribution will be and the maximum stress upon deformation will be minimized to prevent pipe failure due to a shorter moment arms for acting forces.
FIG. 1 illustrates a vertical cross section on an enlarged scale of a sidewall section of one type of prior art double-wall corrugated pipe. The section includes a smooth inner wall 100 and a corrugated outer wall 110. The corrugated outer wall includes corrugation crests 120 and corrugation valleys 130.
In use, it is the deflection and integrity of inner wall 100 that is critical to pipe performance. Deflection of the outer wall 110 is greater than deflection of the inner wall 100 in use, but a certain amount of deflection of the outer corrugated wall 110 is acceptable because, although maintaining the integrity of the outer wall is advantageous, its integrity can be sacrificed to a certain extent without affecting pipe performance, as long as the integrity of the inner wall 100 is maintained. Thus, it is advantageous to provide some flexibility in the outer wall so that it can deflect in use without that deflection translating to the inner wall.
When a pipe is installed in a trench, the hole into which the pipe is placed must be backfilled, for example with the excavated soil. One problem that has been experienced with known corrugated pipe, is that the haunch areas of the ditch are not properly backfilled due to the extremely non-linear outer surface of the corrugated pipe. The excavated material, such as soil, cannot easily pass by the corrugated outer profile of the installed pipe to reach and fill the haunch areas. The effect of this is illustrated in prior art FIGS. 2A and 2B, which show the possible deformation that occurs in an installed pipe after the trench is backfilled. As can be seen, the pipe P does not fill the entire trench area, leaving haunches H between the pipe P and the soil S. When the trench is backfilled, forces on the top of the pipe from the load of the backfill will tend to cause deformation of the pipe, as may the pipe's tendency to settle into the unfilled haunch areas.
It would be beneficial to provide a pipe with an exterior surface that is smoother (less non-linear) so the backfill can more easily reach and fill the haunch areas of the trench, thus limiting or prohibiting sagging of the pipe into unfilled haunch areas.
It would also be beneficial to provide alternative wall designs that increase the moment of inertia of a plastic corrugated pipe so the pipe experiences less deformation in use.